Summer Math Research Program
This is the website for the Northeastern Summer Math Research Program (NSMRP), a paid summer program funded by the math department's Research Training Grant.
Research Experience for Undergraduates
In light of the COVID-19 shutdown, this program was held entirely remotely.
Mon May 4, 9AM: Kick Off Meeting
Mon May 18, 2PM: Preliminary Presentation (20 min/group)
Wed May 27, 2-3PM: Colloquium
Wed June 17, 2-3PM: Colloquium
Thr Jun 25, 2PM: Final Presentations (45 min/group)
Fri July 3: Final Paper Due
Final Paper: The jointly written paper should be at least 10 pages. Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof. No maximum page limit, but writing should be clear and concise.
Final Presentation: (45 for each group). Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.
Participants: Jack Steilberg, Lauren Neudorf. Mentor: Jonier Antunes.
Spectral Graph Theory.
Participants: Ryan Keleti, Noble Mushtak. Mentor: Whitney Drazen.
Participants: Zoe Daunt, Xiaoying He, Xuyang Li. Mentor: Lei Yang.
The RTG group welcomes independent and motivated undergraduates to apply for our Research Experience for Undergraduates (REU). Undergraduate students work with PhD-student mentors for two months during the summer on a research topic, under the supervision of a faculty member. Candidates that are citizens, nationals, or permanent residents of the United States or its territories and possessions are eligible for a scholarship of $2,000 per month.
If you would like to participate in the future, we would welcome you to apply. The application deadline will likely be end of February. You can view the old application form here, though the application may vary.
Potential topics include: Derived categories and homological algebra, Birational geometry and moduli spaces, Hyperkähler manifolds, Moduli theory and enumerative invariants, Hodge theory, Mirror symmetry, Geometric representation theory, Representations of Lie groups and Lie algebras, Quantum groups, Symplectic and Poisson geometry, Geometric quantization, Quantum field theory and string theory, Combinatorial Geometries, Toric Varieties, Arrangements of algebraic varieties.
For more information, please contact MATH-REU@LISTSERV.NEU.EDU
Northeastern University particularly welcomes applications from minorities, women, and persons with disabilities.
Applications are now closed.
The application form asks for a resume and a statement of interest. In your statement of interest, briefly describe some of the following:
What are your goals in the program?
Do you have career plans, and how does this program fit in with them?
Are there specific kinds of math that you have found particularly interesting or enjoyable?
What is your mathematical background?
What else should we know about you that is relevant to your application?
Your statement of interest should be no longer than 1 page.
May 6: First Official REU Meeting (Summer I)
May 13: Proposal Draft
May 28: REU Tea & Colloquium 3-4 PM, Lake 509
June 4: REU Tea & Group Presentations 3-4 PM, Nightingale 544
June 11: REU Tea & Colloquium 3-4 PM, Lake 509
June 21: Final Presentations, Lunch 12-1, Talks 1-4, Lake 509 (Summer I)
June 28: Final Paper Due (Summer I)
August 14: Final Presentations (Summer II)
Final Paper: At least 5 pages. If two students, then paper is written together is at least 10 pages. Should include an introduction with motivation and guiding questions, definitions, examples, a main result and proof. No maximum page limit, but writing should be clear and concise.
Final Presentation: 30 minutes (40 if group of 2). Should introduce audience to area of research, convince them it is interesting through examples, definitions and results. Time is too short to include everything so choose carefully what to present highlighting what you worked hardest on. Narrative and slides and/or boardwork should be clear.
Participants: Hoyin Chu. Mentor: Jonier Antunes. Summer I.
Participants: Noah Fleischmann, Kally Lyonnais. Mentor: Dmytro Matvieievsky. Summer I.
Graph Theory/Chip Firing:
Participants: Kristin Timothy, Michael Wang. Mentor: Ian Dumais. Summer I.
Paper: Sandpiles and Chip Firing.
Participants: Karthik Boyareddygari Mentor: Oleksiy Sorokin. Summer I.
Participants: Walker Miller-Breetz. Mentor: Anupam Kumar. Summer II.
Paper: Cone Points on Algebraic Curves.
The inaugural year of the Northeastern REU had 9 undergraduate participants working in several different areas. The postdoc coordinator was Ivan Martino.
Student: Alon Duvall
Mentor: Brian Hepler
Title: Abstract Regular Polytope
Abstract: Introduction to Abstract Regular Polytopes through a combinatorial geometry approach. C-Groups, Coxeter Groups and 2^k-constructions are also studied.
Student: Kevin Su
Mentor: Jonier Antunes
Abstract: "One of the problems in extremal combinatorics is asking how many edges a graph on n nodes may have while avoiding some speciﬁc subgraphs. For example, Mantel’s theorem says that the most edges a graph on n nodes can have while avoiding K_3 is n^2/4. These statements can also be represented in terms of inequalities of numbers of homomorphisms or in terms of homomorphism densities. Many of these inequalities may be proved using Cauchy-Schwarz (as an inequality on sums of squares) or pictorially due to a gluing algebra on the space of graphs. We summarize some of the graph algebra background involved here and look at how graph limit theory gives a way of proving results in extremal combinatorics."
Student: Timothy Jackman
Mentor: Whitney Drazen
Title: Graph Theory
Abstract: This is an introduction to spectral graph theory until the concepts of (quantum) state transfer.
Student: Felipe Castellano-Macias
Mentor: Alex Sorokin
Title: Leavitt Path Algebras
Abstract. We describe diﬀerent properties of Leavitt path algebras of a graph over a ﬁeld, providing the appropriate background. In addition, we investigate similar results about Leavitt path algebras of a graph over a commutative unital ring. We will mainly explore the connection between the diagonalizability of matrices over a given Leavitt path algebra and the structure of its underlying graph, as well as the classiﬁcation of such algebras up to isomorphism.
Name: Benjamin Bonenfant
Mentor: Reuven Hodges
Student: Walker Miller-Breetz
Mentor: Rahul Singh
Title: Young Tableaux
Abstract: After a short introduction on group theory and group actions, the work focuses on the symmetric group and its action on flagged spaces.
Student: Christina Nguyen
Mentor: Whitney Drazen
Abstract: The main goal of the REU was to obtain a new proof of the non-backtracking version of Ploya’s Theorem for random walks. We began with a discussion of spectral graph theory before studying the backtracking version of Ploya’s Theorem.
Student: Noah Lichtblau
Mentor: Mikhail Mironov
Title: On the Morphism of Schemes
Student: Zheying Yu
Mentor: Celine Bonandrini
Work in a group of three undergraduates with a graduate student group leader
Learn about a topic of active research in mathematics
Pursue hands-on research questions and make original discoveries
Develop your academic writing and presentation skills
Attend biweekly math colloquia
See what math research is all about!
Summer I term: May 4 - June 26
$4000 stipend provided
Rolling application decisions will be made starting February 24, and ending by March 15.
Questions? Contact email@example.com
We particularly welcome applications from students from groups underrepresented in mathematics.
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